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<div class="title">pcl::PolynomialCalculationsT&lt; real &gt; 模板类 参考<div class="ingroups"><a class="el" href="group__common.html">Common components</a></div></div>  </div>
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<p>This provides some functionality for polynomials, like finding roots or approximating bivariate polynomials  
 <a href="classpcl_1_1_polynomial_calculations_t.html#details">更多...</a></p>

<p><code>#include &lt;<a class="el" href="polynomial__calculations_8h_source.html">polynomial_calculations.h</a>&gt;</code></p>
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类</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structpcl_1_1_polynomial_calculations_t_1_1_parameters.html">Parameters</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a class="el" href="structpcl_1_1_polynomial_calculations_t_1_1_parameters.html" title="Parameters used in this class">Parameters</a> used in this class  <a href="structpcl_1_1_polynomial_calculations_t_1_1_parameters.html#details">更多...</a><br /></td></tr>
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Public 成员函数</h2></td></tr>
<tr class="memitem:a8a0f1e9bc452a562226ba3d049fcec25"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classpcl_1_1_polynomial_calculations_t.html#a8a0f1e9bc452a562226ba3d049fcec25">solveQuarticEquation</a> (real a, real b, real c, real d, real e, std::vector&lt; real &gt; &amp;roots) const</td></tr>
<tr class="separator:a8a0f1e9bc452a562226ba3d049fcec25"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a062e05d7e022faf66c9d2e6eb0bc1d7c"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classpcl_1_1_polynomial_calculations_t.html#a062e05d7e022faf66c9d2e6eb0bc1d7c">solveCubicEquation</a> (real a, real b, real c, real d, std::vector&lt; real &gt; &amp;roots) const</td></tr>
<tr class="separator:a062e05d7e022faf66c9d2e6eb0bc1d7c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9ef9dc239623c784175b661528dc7407"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classpcl_1_1_polynomial_calculations_t.html#a9ef9dc239623c784175b661528dc7407">solveQuadraticEquation</a> (real a, real b, real c, std::vector&lt; real &gt; &amp;roots) const</td></tr>
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<tr class="memitem:ac3a6930b43244acfd47335970abf0723"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classpcl_1_1_polynomial_calculations_t.html#ac3a6930b43244acfd47335970abf0723">solveLinearEquation</a> (real a, real b, std::vector&lt; real &gt; &amp;roots) const</td></tr>
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<tr class="memitem:a694d2f980ff0379e91113472dfd7febe"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classpcl_1_1_bivariate_polynomial_t.html">BivariatePolynomialT</a>&lt; real &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classpcl_1_1_polynomial_calculations_t.html#a694d2f980ff0379e91113472dfd7febe">bivariatePolynomialApproximation</a> (std::vector&lt; Eigen::Matrix&lt; real, 3, 1 &gt;, Eigen::aligned_allocator&lt; Eigen::Matrix&lt; real, 3, 1 &gt; &gt; &gt; &amp;samplePoints, unsigned int polynomial_degree, bool &amp;error) const</td></tr>
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<tr class="memitem:a853732c067ecc8f1082fb68fcd961c53"><td class="memItemLeft" align="right" valign="top"><a id="a853732c067ecc8f1082fb68fcd961c53"></a>
bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classpcl_1_1_polynomial_calculations_t.html#a853732c067ecc8f1082fb68fcd961c53">bivariatePolynomialApproximation</a> (std::vector&lt; Eigen::Matrix&lt; real, 3, 1 &gt;, Eigen::aligned_allocator&lt; Eigen::Matrix&lt; real, 3, 1 &gt; &gt; &gt; &amp;samplePoints, unsigned int polynomial_degree, <a class="el" href="classpcl_1_1_bivariate_polynomial_t.html">BivariatePolynomialT</a>&lt; real &gt; &amp;ret) const</td></tr>
<tr class="memdesc:a853732c067ecc8f1082fb68fcd961c53"><td class="mdescLeft">&#160;</td><td class="mdescRight">Same as above, using a reference for the return value <br /></td></tr>
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void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classpcl_1_1_polynomial_calculations_t.html#a1e4c691ae491f88269108631681867f2">setZeroValue</a> (real new_zero_value)</td></tr>
<tr class="memdesc:a1e4c691ae491f88269108631681867f2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Set the minimum value under which values are considered zero <br /></td></tr>
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bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (real d) const</td></tr>
<tr class="memdesc:a22edebe53e66d99ae1ad45e8b8cb790a"><td class="mdescLeft">&#160;</td><td class="mdescRight">check if fabs(d)&lt;zeroValue <br /></td></tr>
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bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classpcl_1_1_polynomial_calculations_t.html#a84239daee976d1a6c57fbd31a531764e">sqrtIsNearlyZero</a> (real d) const</td></tr>
<tr class="memdesc:a84239daee976d1a6c57fbd31a531764e"><td class="mdescLeft">&#160;</td><td class="mdescRight">check if sqrt(fabs(d))&lt;zeroValue <br /></td></tr>
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<a class="el" href="structpcl_1_1_polynomial_calculations_t_1_1_parameters.html">Parameters</a>&#160;</td><td class="memItemRight" valign="bottom"><b>parameters_</b></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">详细描述</h2>
<div class="textblock"><h3>template&lt;typename real&gt;<br />
class pcl::PolynomialCalculationsT&lt; real &gt;</h3>

<p>This provides some functionality for polynomials, like finding roots or approximating bivariate polynomials </p>
<dl class="section author"><dt>作者</dt><dd>Bastian Steder </dd></dl>
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<h2 class="memtitle"><span class="permalink"><a href="#a694d2f980ff0379e91113472dfd7febe">&#9670;&nbsp;</a></span>bivariatePolynomialApproximation()</h2>

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          <td class="memname"><a class="el" href="classpcl_1_1_bivariate_polynomial_t.html">pcl::BivariatePolynomialT</a>&lt; real &gt; <a class="el" href="classpcl_1_1_polynomial_calculations_t.html">pcl::PolynomialCalculationsT</a>&lt; real &gt;::bivariatePolynomialApproximation </td>
          <td>(</td>
          <td class="paramtype">std::vector&lt; Eigen::Matrix&lt; real, 3, 1 &gt;, Eigen::aligned_allocator&lt; Eigen::Matrix&lt; real, 3, 1 &gt; &gt; &gt; &amp;&#160;</td>
          <td class="paramname"><em>samplePoints</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">unsigned int&#160;</td>
          <td class="paramname"><em>polynomial_degree</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">bool &amp;&#160;</td>
          <td class="paramname"><em>error</em>&#160;</td>
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          <td></td>
          <td>)</td>
          <td></td><td> const</td>
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<p>Get the bivariate polynomial approximation for Z(X,Y) from the given sample points. The parameters a,b,c,... for the polynom are returned. The order is, e.g., for degree 1: ax+by+c and for degree 2: ax²+bxy+cx+dy²+ey+f. error is set to true if the approximation did not work for any reason (not enough points, matrix not invertible, etc.) </p>
<div class="fragment"><div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;{</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;  <a class="code" href="classpcl_1_1_bivariate_polynomial_t.html">pcl::BivariatePolynomialT&lt;real&gt;</a> ret;</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;  error = <a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a694d2f980ff0379e91113472dfd7febe">bivariatePolynomialApproximation</a> (samplePoints, polynomial_degree, ret);</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;  <span class="keywordflow">return</span> ret;</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;}</div>
<div class="ttc" id="aclasspcl_1_1_bivariate_polynomial_t_html"><div class="ttname"><a href="classpcl_1_1_bivariate_polynomial_t.html">pcl::BivariatePolynomialT</a></div><div class="ttdoc">This represents a bivariate polynomial and provides some functionality for it</div><div class="ttdef"><b>Definition:</b> bivariate_polynomial.h:53</div></div>
<div class="ttc" id="aclasspcl_1_1_polynomial_calculations_t_html_a694d2f980ff0379e91113472dfd7febe"><div class="ttname"><a href="classpcl_1_1_polynomial_calculations_t.html#a694d2f980ff0379e91113472dfd7febe">pcl::PolynomialCalculationsT::bivariatePolynomialApproximation</a></div><div class="ttdeci">BivariatePolynomialT&lt; real &gt; bivariatePolynomialApproximation(std::vector&lt; Eigen::Matrix&lt; real, 3, 1 &gt;, Eigen::aligned_allocator&lt; Eigen::Matrix&lt; real, 3, 1 &gt; &gt; &gt; &amp;samplePoints, unsigned int polynomial_degree, bool &amp;error) const</div><div class="ttdef"><b>Definition:</b> polynomial_calculations.hpp:374</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a062e05d7e022faf66c9d2e6eb0bc1d7c">&#9670;&nbsp;</a></span>solveCubicEquation()</h2>

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          <td class="memname">void <a class="el" href="classpcl_1_1_polynomial_calculations_t.html">pcl::PolynomialCalculationsT</a>&lt; real &gt;::solveCubicEquation </td>
          <td>(</td>
          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>a</em>, </td>
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          <td class="paramkey"></td>
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          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>b</em>, </td>
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          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>c</em>, </td>
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          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>d</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">std::vector&lt; real &gt; &amp;&#160;</td>
          <td class="paramname"><em>roots</em>&#160;</td>
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          <td></td>
          <td>)</td>
          <td></td><td> const</td>
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<p>Solves an equation of the form ax^3 + bx^2 + cx + d = 0 See <a href="http://en.wikipedia.org/wiki/Cubic_equation">http://en.wikipedia.org/wiki/Cubic_equation</a> </p>
<div class="fragment"><div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;{</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  <span class="comment">//cout &lt;&lt; &quot;Trying to solve &quot;&lt;&lt;a&lt;&lt;&quot;x^3 + &quot;&lt;&lt;b&lt;&lt;&quot;x^2 + &quot;&lt;&lt;c&lt;&lt;&quot;x + &quot;&lt;&lt;d&lt;&lt;&quot; = 0\n&quot;;</span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160; </div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;  <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (a))</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;  {</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    <span class="comment">//cout &lt;&lt; &quot;Highest order element is 0 =&gt; Calling solveQuadraticEquation.\n&quot;;</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    <a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a9ef9dc239623c784175b661528dc7407">solveQuadraticEquation</a> (b, c, d, roots);</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  }</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160; </div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (d))</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;  {</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    roots.push_back (0.0);</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    <span class="comment">//cout &lt;&lt; &quot;Constant element is 0 =&gt; Adding root 0 and calling solveQuadraticEquation.\n&quot;;</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    std::vector&lt;real&gt; tmpRoots;</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    <a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a9ef9dc239623c784175b661528dc7407">solveQuadraticEquation</a> (a, b, c, tmpRoots);</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;tmpRoots.size (); i++)</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;      <span class="keywordflow">if</span> (!<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (tmpRoots[i]))</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;        roots.push_back (tmpRoots[i]);</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;  }</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160; </div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;  <span class="keywordtype">double</span> a2 = a*a,</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;         a3 = a2*a,</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;         b2 = b*b,</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;         b3 = b2*b,</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;         alpha = ( (3.0*a*c-b2)/ (3.0*a2)),</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;         beta  = (2*b3/ (27.0*a3)) - ( (b*c)/ (3.0*a2)) + (d/a),</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;         alpha2 = alpha*alpha,</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;         alpha3 = alpha2*alpha,</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;         beta2 = beta*beta;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;  </div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;  <span class="comment">// Value for resubstitution:</span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;  <span class="keywordtype">double</span> resubValue = b/ (3*a);</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160; </div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;  <span class="comment">//cout &lt;&lt; &quot;Trying to solve y^3 + &quot;&lt;&lt;alpha&lt;&lt;&quot;y + &quot;&lt;&lt;beta&lt;&lt;&quot;\n&quot;;</span></div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160; </div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  <span class="keywordtype">double</span> discriminant = (alpha3/27.0) + 0.25*beta2;</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160; </div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;  <span class="comment">//cout &lt;&lt; &quot;Discriminant is &quot;&lt;&lt;discriminant&lt;&lt;&quot;\n&quot;;</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160; </div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;  <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (discriminant))</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;  {</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    <span class="keywordflow">if</span> (!<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (alpha) || !<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (beta))</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    {</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;      roots.push_back ( (-3.0*beta)/ (2.0*alpha) - resubValue);</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;      roots.push_back ( (3.0*beta)/alpha - resubValue);</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    }</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;    {</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;      roots.push_back (-resubValue);</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;    }</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  }</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (discriminant &gt; 0)</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;  {</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    <span class="keywordtype">double</span> sqrtDiscriminant = sqrt (discriminant);</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <span class="keywordtype">double</span> d1 = -0.5*beta + sqrtDiscriminant,</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;           d2 = -0.5*beta - sqrtDiscriminant;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    <span class="keywordflow">if</span> (d1 &lt; 0)</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;      d1 = -pow (-d1, 1.0/3.0);</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;      d1 = pow (d1, 1.0/3.0);</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160; </div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;    <span class="keywordflow">if</span> (d2 &lt; 0)</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;      d2 = -pow (-d2, 1.0/3.0);</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;      d2 = pow (d2, 1.0/3.0);</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160; </div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    <span class="comment">//cout &lt;&lt; PVAR (d1)&lt;&lt;&quot;, &quot;&lt;&lt;PVAR (d2)&lt;&lt;&quot;\n&quot;;</span></div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;    roots.push_back (d1 + d2 - resubValue);</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;  }</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;  {</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    <span class="keywordtype">double</span> tmp1 = sqrt (- (4.0/3.0)*alpha),</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;           tmp2 = acos (-sqrt (-27.0/alpha3)*0.5*beta)/3.0;</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;    roots.push_back (tmp1*cos (tmp2) - resubValue);</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    roots.push_back (-tmp1*cos (tmp2 + M_PI/3.0) - resubValue);</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    roots.push_back (-tmp1*cos (tmp2 - M_PI/3.0) - resubValue);</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  }</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160; </div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;<span class="preprocessor">#if 0</span></div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  cout &lt;&lt; __PRETTY_FUNCTION__ &lt;&lt; <span class="stringliteral">&quot;: Found &quot;</span>&lt;&lt;roots.size ()&lt;&lt;<span class="stringliteral">&quot; roots.\n&quot;</span>;</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;roots.size (); i++)</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;  {</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    real x=roots[i], x2=x*x, x3=x2*x;</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    real result = a*x3 + b*x2 + c*x + d;</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    <span class="keywordflow">if</span> (fabs (result) &gt; 1e-4)</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    {</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;      cout &lt;&lt; <span class="stringliteral">&quot;Something went wrong:\n&quot;</span>;</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;      <span class="comment">//roots.clear ();</span></div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    }</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    cout &lt;&lt; <span class="stringliteral">&quot;Root &quot;</span>&lt;&lt;i&lt;&lt;<span class="stringliteral">&quot; = &quot;</span>&lt;&lt;roots[i]&lt;&lt;<span class="stringliteral">&quot;. (&quot;</span>&lt;&lt;a&lt;&lt;<span class="stringliteral">&quot;x^3 + &quot;</span>&lt;&lt;b&lt;&lt;<span class="stringliteral">&quot;x^2 + &quot;</span>&lt;&lt;c&lt;&lt;<span class="stringliteral">&quot;x + &quot;</span>&lt;&lt;d&lt;&lt;<span class="stringliteral">&quot; = &quot;</span>&lt;&lt;result&lt;&lt;<span class="stringliteral">&quot;)\n&quot;</span>;</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;  }</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;}</div>
<div class="ttc" id="aclasspcl_1_1_polynomial_calculations_t_html_a22edebe53e66d99ae1ad45e8b8cb790a"><div class="ttname"><a href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">pcl::PolynomialCalculationsT::isNearlyZero</a></div><div class="ttdeci">bool isNearlyZero(real d) const</div><div class="ttdoc">check if fabs(d)&lt;zeroValue</div><div class="ttdef"><b>Definition:</b> polynomial_calculations.h:112</div></div>
<div class="ttc" id="aclasspcl_1_1_polynomial_calculations_t_html_a9ef9dc239623c784175b661528dc7407"><div class="ttname"><a href="classpcl_1_1_polynomial_calculations_t.html#a9ef9dc239623c784175b661528dc7407">pcl::PolynomialCalculationsT::solveQuadraticEquation</a></div><div class="ttdeci">void solveQuadraticEquation(real a, real b, real c, std::vector&lt; real &gt; &amp;roots) const</div><div class="ttdef"><b>Definition:</b> polynomial_calculations.hpp:62</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ac3a6930b43244acfd47335970abf0723">&#9670;&nbsp;</a></span>solveLinearEquation()</h2>

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template&lt;typename real &gt; </div>
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          <td class="memname">void <a class="el" href="classpcl_1_1_polynomial_calculations_t.html">pcl::PolynomialCalculationsT</a>&lt; real &gt;::solveLinearEquation </td>
          <td>(</td>
          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>a</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>b</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">std::vector&lt; real &gt; &amp;&#160;</td>
          <td class="paramname"><em>roots</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td> const</td>
        </tr>
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<p>Solves an equation of the form ax + b = 0 </p>
<div class="fragment"><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;{</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;  <span class="comment">//cout &lt;&lt; &quot;Trying to solve &quot;&lt;&lt;a&lt;&lt;&quot;x + &quot;&lt;&lt;b&lt;&lt;&quot; = 0\n&quot;;</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (b))</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;  {</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    roots.push_back (0.0);</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;  }</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;  <span class="keywordflow">if</span> (!<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (a/b))</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;  {</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    roots.push_back (-b/a);</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;  }</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;  </div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="preprocessor">#if 0</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;  cout &lt;&lt; __PRETTY_FUNCTION__ &lt;&lt; <span class="stringliteral">&quot;: Found &quot;</span>&lt;&lt;roots.size ()&lt;&lt;<span class="stringliteral">&quot; roots.\n&quot;</span>;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;roots.size (); i++)</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;  {</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    real x=roots[i];</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    real result = a*x + b;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    <span class="keywordflow">if</span> (!<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (result))</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    {</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;      cout &lt;&lt; <span class="stringliteral">&quot;Something went wrong during solving of polynomial &quot;</span>&lt;&lt;a&lt;&lt;<span class="stringliteral">&quot;x + &quot;</span>&lt;&lt;b&lt;&lt;<span class="stringliteral">&quot; = 0\n&quot;</span>;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;      <span class="comment">//roots.clear ();</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    }</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    cout &lt;&lt; <span class="stringliteral">&quot;Root &quot;</span>&lt;&lt;i&lt;&lt;<span class="stringliteral">&quot; = &quot;</span>&lt;&lt;roots[i]&lt;&lt;<span class="stringliteral">&quot;. (&quot;</span>&lt;&lt;a&lt;&lt;<span class="stringliteral">&quot;x^ + &quot;</span>&lt;&lt;b&lt;&lt;<span class="stringliteral">&quot; = &quot;</span>&lt;&lt;result&lt;&lt;<span class="stringliteral">&quot;)\n&quot;</span>;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;  }</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9ef9dc239623c784175b661528dc7407">&#9670;&nbsp;</a></span>solveQuadraticEquation()</h2>

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template&lt;typename real &gt; </div>
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          <td class="memname">void <a class="el" href="classpcl_1_1_polynomial_calculations_t.html">pcl::PolynomialCalculationsT</a>&lt; real &gt;::solveQuadraticEquation </td>
          <td>(</td>
          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>a</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>b</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>c</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">std::vector&lt; real &gt; &amp;&#160;</td>
          <td class="paramname"><em>roots</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td> const</td>
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<p>Solves an equation of the form ax^2 + bx + c = 0 See <a href="http://en.wikipedia.org/wiki/Quadratic_equation">http://en.wikipedia.org/wiki/Quadratic_equation</a> </p>
<div class="fragment"><div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;{</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  <span class="comment">//cout &lt;&lt; &quot;Trying to solve &quot;&lt;&lt;a&lt;&lt;&quot;x^2 + &quot;&lt;&lt;b&lt;&lt;&quot;x + &quot;&lt;&lt;c&lt;&lt;&quot; = 0\n&quot;;</span></div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (a))</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  {</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="comment">//cout &lt;&lt; &quot;Highest order element is 0 =&gt; Calling solveLineaqrEquation.\n&quot;;</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    <a class="code" href="classpcl_1_1_polynomial_calculations_t.html#ac3a6930b43244acfd47335970abf0723">solveLinearEquation</a> (b, c, roots);</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;  }</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160; </div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;  <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (c))</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;  {</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    roots.push_back (0.0);</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <span class="comment">//cout &lt;&lt; &quot;Constant element is 0 =&gt; Adding root 0 and calling solveLinearEquation.\n&quot;;</span></div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    std::vector&lt;real&gt; tmpRoots;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <a class="code" href="classpcl_1_1_polynomial_calculations_t.html#ac3a6930b43244acfd47335970abf0723">solveLinearEquation</a> (a, b, tmpRoots);</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;tmpRoots.size (); i++)</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;      <span class="keywordflow">if</span> (!<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (tmpRoots[i]))</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;        roots.push_back (tmpRoots[i]);</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  }</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160; </div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;  real tmp = b*b - 4*a*c;</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  <span class="keywordflow">if</span> (tmp&gt;0)</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;  {</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    tmp = sqrt (tmp);</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    real tmp2 = 1.0/ (2*a);</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    roots.push_back ( (-b + tmp)*tmp2);</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    roots.push_back ( (-b - tmp)*tmp2);</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  }</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a84239daee976d1a6c57fbd31a531764e">sqrtIsNearlyZero</a> (tmp))</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  {</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    roots.push_back (-b/ (2*a));</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  }</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160; </div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;<span class="preprocessor">#if 0</span></div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  cout &lt;&lt; __PRETTY_FUNCTION__ &lt;&lt; <span class="stringliteral">&quot;: Found &quot;</span>&lt;&lt;roots.size ()&lt;&lt;<span class="stringliteral">&quot; roots.\n&quot;</span>;</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;roots.size (); i++)</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  {</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    real x=roots[i], x2=x*x;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    real result = a*x2 + b*x + c;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    <span class="keywordflow">if</span> (!<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (result))</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    {</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;      cout &lt;&lt; <span class="stringliteral">&quot;Something went wrong during solving of polynomial &quot;</span>&lt;&lt;a&lt;&lt;<span class="stringliteral">&quot;x^2 + &quot;</span>&lt;&lt;b&lt;&lt;<span class="stringliteral">&quot;x + &quot;</span>&lt;&lt;c&lt;&lt;<span class="stringliteral">&quot; = 0\n&quot;</span>;</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;      <span class="comment">//roots.clear ();</span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;    }</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <span class="comment">//cout &lt;&lt; &quot;Root &quot;&lt;&lt;i&lt;&lt;&quot; = &quot;&lt;&lt;roots[i]&lt;&lt;&quot;. (&quot;&lt;&lt;a&lt;&lt;&quot;x^2 + &quot;&lt;&lt;b&lt;&lt;&quot;x + &quot;&lt;&lt;c&lt;&lt;&quot; = &quot;&lt;&lt;result&lt;&lt;&quot;)\n&quot;;</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;  }</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;}</div>
<div class="ttc" id="aclasspcl_1_1_polynomial_calculations_t_html_a84239daee976d1a6c57fbd31a531764e"><div class="ttname"><a href="classpcl_1_1_polynomial_calculations_t.html#a84239daee976d1a6c57fbd31a531764e">pcl::PolynomialCalculationsT::sqrtIsNearlyZero</a></div><div class="ttdeci">bool sqrtIsNearlyZero(real d) const</div><div class="ttdoc">check if sqrt(fabs(d))&lt;zeroValue</div><div class="ttdef"><b>Definition:</b> polynomial_calculations.h:119</div></div>
<div class="ttc" id="aclasspcl_1_1_polynomial_calculations_t_html_ac3a6930b43244acfd47335970abf0723"><div class="ttname"><a href="classpcl_1_1_polynomial_calculations_t.html#ac3a6930b43244acfd47335970abf0723">pcl::PolynomialCalculationsT::solveLinearEquation</a></div><div class="ttdeci">void solveLinearEquation(real a, real b, std::vector&lt; real &gt; &amp;roots) const</div><div class="ttdef"><b>Definition:</b> polynomial_calculations.hpp:29</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a8a0f1e9bc452a562226ba3d049fcec25">&#9670;&nbsp;</a></span>solveQuarticEquation()</h2>

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template&lt;typename real &gt; </div>
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          <td class="memname">void <a class="el" href="classpcl_1_1_polynomial_calculations_t.html">pcl::PolynomialCalculationsT</a>&lt; real &gt;::solveQuarticEquation </td>
          <td>(</td>
          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>a</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>b</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>c</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>d</em>, </td>
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          <td></td>
          <td class="paramtype">real&#160;</td>
          <td class="paramname"><em>e</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">std::vector&lt; real &gt; &amp;&#160;</td>
          <td class="paramname"><em>roots</em>&#160;</td>
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          <td></td>
          <td>)</td>
          <td></td><td> const</td>
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<p>Solves an equation of the form ax^4 + bx^3 + cx^2 +dx + e = 0 See <a href="http://en.wikipedia.org/wiki/Quartic_equation#Summary_of_Ferrari.27s_method">http://en.wikipedia.org/wiki/Quartic_equation#Summary_of_Ferrari.27s_method</a> </p>
<div class="fragment"><div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;{</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  <span class="comment">//cout &lt;&lt; &quot;Trying to solve &quot;&lt;&lt;a&lt;&lt;&quot;x^4 + &quot;&lt;&lt;b&lt;&lt;&quot;x^3 + &quot;&lt;&lt;c&lt;&lt;&quot;x^2 + &quot;&lt;&lt;d&lt;&lt;&quot;x + &quot;&lt;&lt;e&lt;&lt;&quot; = 0\n&quot;;</span></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160; </div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;  <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (a))</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;  {</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    <span class="comment">//cout &lt;&lt; &quot;Highest order element is 0 =&gt; Calling solveCubicEquation.\n&quot;;</span></div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;    <a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a062e05d7e022faf66c9d2e6eb0bc1d7c">solveCubicEquation</a> (b, c, d, e, roots);</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;  } </div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160; </div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;  <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (e))</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;  {</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;    roots.push_back (0.0);</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;    <span class="comment">//cout &lt;&lt; &quot;Constant element is 0 =&gt; Adding root 0 and calling solveCubicEquation.\n&quot;;</span></div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;    std::vector&lt;real&gt; tmpRoots;</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;    <a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a062e05d7e022faf66c9d2e6eb0bc1d7c">solveCubicEquation</a> (a, b, c, d, tmpRoots);</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;tmpRoots.size (); i++)</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;      <span class="keywordflow">if</span> (!<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (tmpRoots[i]))</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;        roots.push_back (tmpRoots[i]);</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;  } </div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160; </div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;  <span class="keywordtype">double</span> root1, root2, root3, root4,</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;         a2 = a*a,</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;         a3 = a2*a,</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;         a4 = a2*a2,</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;         b2 = b*b,</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;         b3 = b2*b,</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;         b4 = b2*b2,</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;         alpha = ( (-3.0*b2)/ (8.0*a2)) + (c/a),</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;         beta  = (b3/ (8.0*a3)) - ( (b*c)/ (2.0*a2)) + (d/a),</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;         gamma = ( (-3.0*b4)/ (256.0*a4)) + ( (c*b2)/ (16.0*a3)) - ( (b*d)/ (4.0*a2)) + (e/a),</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;         alpha2 = alpha*alpha;</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  </div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;  <span class="comment">// Value for resubstitution:</span></div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;  <span class="keywordtype">double</span> resubValue = b/ (4*a);</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160; </div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;  <span class="comment">//cout &lt;&lt; &quot;Trying to solve y^4 + &quot;&lt;&lt;alpha&lt;&lt;&quot;y^2 + &quot;&lt;&lt;beta&lt;&lt;&quot;y + &quot;&lt;&lt;gamma&lt;&lt;&quot;\n&quot;;</span></div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;  </div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;  <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (beta))</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;  {  <span class="comment">// y^4 + alpha*y^2 + gamma\n&quot;;</span></div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;    <span class="comment">//cout &lt;&lt; &quot;Using beta=0 condition\n&quot;;</span></div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;    std::vector&lt;real&gt; tmpRoots;</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;    <a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a9ef9dc239623c784175b661528dc7407">solveQuadraticEquation</a> (1.0, alpha, gamma, tmpRoots);</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;tmpRoots.size (); i++)</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;    {</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;      <span class="keywordtype">double</span> qudraticRoot = tmpRoots[i];</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;      <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a84239daee976d1a6c57fbd31a531764e">sqrtIsNearlyZero</a> (qudraticRoot))</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;      {</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;        roots.push_back (-resubValue);</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;      }</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;      <span class="keywordflow">else</span> <span class="keywordflow">if</span> (qudraticRoot &gt; 0.0)</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;      {</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;        root1 = sqrt (qudraticRoot);</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;        roots.push_back (root1 - resubValue);</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;        roots.push_back (-root1 - resubValue);</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;      }</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    }</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;  }</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;  {</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;    <span class="comment">//cout &lt;&lt; &quot;beta != 0\n&quot;;</span></div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;    <span class="keywordtype">double</span> alpha3 = alpha2*alpha,</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;           beta2 = beta*beta,</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;           p = (-alpha2/12.0)-gamma,</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;           q = (-alpha3/108.0)+ ( (alpha*gamma)/3.0)- (beta2/8.0),</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;           q2 = q*q,</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;           p3 = p*p*p,</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;           u = (0.5*q) + sqrt ( (0.25*q2)+ (p3/27.0));</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;    <span class="keywordflow">if</span> (u &gt; 0.0)</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;      u = pow (u, 1.0/3.0);</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (u))</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;      u = 0.0;</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;      u = -pow (-u, 1.0/3.0);</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160; </div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;    <span class="keywordtype">double</span> y = (-5.0/6.0)*alpha - u;</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;    <span class="keywordflow">if</span> (!<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (u))</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;      y += p/ (3.0*u);</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160; </div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;    <span class="keywordtype">double</span> w = alpha + 2.0*y;</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;    </div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;    <span class="keywordflow">if</span> (w &gt; 0)</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;    {</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;      w = sqrt (w);</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    }</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (w))</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;    {</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;      w = 0;</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    }</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;    {</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;      <span class="comment">//cout &lt;&lt; &quot;Found no roots\n&quot;;</span></div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;      <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;    }</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160; </div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;    <span class="keywordtype">double</span> tmp1 = - (3.0*alpha + 2.0*y + 2.0* (beta/w)),</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;           tmp2 = - (3.0*alpha + 2.0*y - 2.0* (beta/w));</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;    </div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;    <span class="keywordflow">if</span> (tmp1 &gt; 0)</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;    {</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;      tmp1 = sqrt (tmp1);</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;      root1 = - (b/ (4.0*a)) + 0.5* (w+tmp1);</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;      root2 = - (b/ (4.0*a)) + 0.5* (w-tmp1);</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;      roots.push_back (root1);</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;      roots.push_back (root2);</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;    }</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (tmp1))</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;    {</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;      root1 = - (b/ (4.0*a)) + 0.5*w;</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;      roots.push_back (root1);</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;    }</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160; </div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;   <span class="keywordflow">if</span> (tmp2 &gt; 0)</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;   {</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;      tmp2 = sqrt (tmp2);</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;      root3 = - (b/ (4.0*a)) + 0.5* (-w+tmp2);</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;      root4 = - (b/ (4.0*a)) + 0.5* (-w-tmp2);</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;      roots.push_back (root3);</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;      roots.push_back (root4);</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;    }</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code" href="classpcl_1_1_polynomial_calculations_t.html#a22edebe53e66d99ae1ad45e8b8cb790a">isNearlyZero</a> (tmp2))</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;    {</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;      root3 = - (b/ (4.0*a)) - 0.5*w;</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;      roots.push_back (root3);</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;    }</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;   </div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;    <span class="comment">//cout &lt;&lt; &quot;Test: &quot; &lt;&lt; alpha&lt;&lt;&quot;, &quot;&lt;&lt;beta&lt;&lt;&quot;, &quot;&lt;&lt;gamma&lt;&lt;&quot;, &quot;&lt;&lt;p&lt;&lt;&quot;, &quot;&lt;&lt;q&lt;&lt;&quot;, &quot;&lt;&lt;u &lt;&lt;&quot;, &quot;&lt;&lt;y&lt;&lt;&quot;, &quot;&lt;&lt;w&lt;&lt;&quot;\n&quot;;</span></div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;  }</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;  </div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;<span class="preprocessor">#if 0</span></div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;  cout &lt;&lt; __PRETTY_FUNCTION__ &lt;&lt; <span class="stringliteral">&quot;: Found &quot;</span>&lt;&lt;roots.size ()&lt;&lt;<span class="stringliteral">&quot; roots.\n&quot;</span>;</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i=0; i&lt;roots.size (); i++)</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;  {</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;    real x=roots[i], x2=x*x, x3=x2*x, x4=x2*x2;</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;    real result = a*x4 + b*x3 + c*x2 + d*x + e;</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;    <span class="keywordflow">if</span> (fabs (result) &gt; 1e-4)</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;    {</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;      cout &lt;&lt; <span class="stringliteral">&quot;Something went wrong:\n&quot;</span>;</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;      <span class="comment">//roots.clear ();</span></div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;    }</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    cout &lt;&lt; <span class="stringliteral">&quot;Root &quot;</span>&lt;&lt;i&lt;&lt;<span class="stringliteral">&quot; = &quot;</span>&lt;&lt;roots[i]</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;         &lt;&lt; <span class="stringliteral">&quot;. (&quot;</span>&lt;&lt;a&lt;&lt;<span class="stringliteral">&quot;x^4 + &quot;</span>&lt;&lt;b&lt;&lt;<span class="stringliteral">&quot;x^3 + &quot;</span>&lt;&lt;c&lt;&lt;<span class="stringliteral">&quot;x^2 + &quot;</span>&lt;&lt;d&lt;&lt;<span class="stringliteral">&quot;x + &quot;</span>&lt;&lt;e&lt;&lt;<span class="stringliteral">&quot; = &quot;</span>&lt;&lt;result&lt;&lt;<span class="stringliteral">&quot;)\n&quot;</span>;</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;  }</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;  cout &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;}</div>
<div class="ttc" id="aclasspcl_1_1_polynomial_calculations_t_html_a062e05d7e022faf66c9d2e6eb0bc1d7c"><div class="ttname"><a href="classpcl_1_1_polynomial_calculations_t.html#a062e05d7e022faf66c9d2e6eb0bc1d7c">pcl::PolynomialCalculationsT::solveCubicEquation</a></div><div class="ttdeci">void solveCubicEquation(real a, real b, real c, real d, std::vector&lt; real &gt; &amp;roots) const</div><div class="ttdef"><b>Definition:</b> polynomial_calculations.hpp:118</div></div>
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